Most of the results presented in the past on the tearing-mode phenomenology have been obtained by neglecting the local properties of the current profile at the reconnecting surface. In this paper we study the properties of the instability using numerical techniques. We adopt a planar equilibrium configuration which can be made asymmetric with respect to the resonant layer by changing the value of the local current gradient. We show that the local current gradients can modify the growth rate of the mode considerably. This means that in more realistic geometries, where the asymmetries are intrinsically present, the classical dispersion relation of Furthet al. has to be modified.